An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

Sihun Jo; Minsuk Yang

doi:10.1016/j.jmaa.2014.01.040

paper

An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

arXiv:1606.01179 · doi:10.1016/j.jmaa.2014.01.040

Abstract

We investigate the second moment of a random sampling $ζ (1/2 + i X_{t})$ of the Riemann zeta function on the critical line. Our main result states that if $X_{t}$ is an increasing random sampling with gamma distribution, then for all sufficiently large $t$ , \[\mathbb{E} |ζ(1/2+iX_t)|^2 = \log t + O(\sqrt{\log t}\log\log t).\]

13 pages